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Chords of semisept

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Below are listed the dyadic chords of 11-limit semisept temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 540/539 are swetismic, and by 176/175 valinorsmic.

Semisept has MOS of size 5, 8, 13, 18, 31, 49 and 80. Some amount triadic and tetradic harmony shows itself by the 13-note MOS and much more with 18 notes. The swetismic tetrad with complexity 11 is worthy of particular note.

Triads

Number
 Chord
 Transversal
 Type
1
 0-2-9
 1-12/7-7/5
 swetismic
2
 0-7-9
 1-18/11-7/5
 swetismic
3
 0-2-11
 1-12/7-6/5
 utonal
4
 0-9-11
 1-7/5-6/5
 otonal
5
 0-2-12
 1-12/7-11/7
 otonal
6
 0-6-12
 1-5/4-11/7
 valinorsmic
7
 0-10-12
 1-11/6-11/7
 utonal
8
 0-6-15
 1-5/4-7/4
 otonal
9
 0-9-15
 1-7/5-7/4
 utonal
10
 0-2-17
 1-12/7-3/2
 utonal
11
 0-6-17
 1-5/4-3/2
 otonal
12
 0-7-17
 1-18/11-3/2
 utonal
13
 0-10-17
 1-11/6-3/2
 otonal
14
 0-11-17
 1-6/5-3/2
 utonal
15
 0-15-17
 1-7/4-3/2
 otonal
16
 0-2-19
 1-12/7-9/7
 otonal
17
 0-7-19
 1-18/11-9/7
 utonal
18
 0-9-19
 1-7/5-9/7
 swetismic
19
 0-10-19
 1-11/6-9/7
 swetismic
20
 0-12-19
 1-11/7-9/7
 otonal
21
 0-17-19
 1-3/2-9/7
 utonal
22
 0-2-21
 1-12/7-11/10
 swetismic
23
 0-6-21
 1-5/4-11/10
 valinorsmic
24
 0-9-21
 1-7/5-11/10
 otonal
25
 0-10-21
 1-11/6-11/10
 utonal
26
 0-11-21
 1-6/5-11/10
 otonal
27
 0-12-21
 1-11/7-11/10
 utonal
28
 0-15-21
 1-7/4-11/10
 valinorsmic
29
 0-19-21
 1-9/7-11/10
 swetismic
30
 0-6-27
 1-5/4-11/8
 otonal
31
 0-10-27
 1-11/6-11/8
 utonal
32
 0-12-27
 1-11/7-11/8
 utonal
33
 0-15-27
 1-7/4-11/8
 otonal
34
 0-17-27
 1-3/2-11/8
 otonal
35
 0-21-27
 1-11/10-11/8
 utonal
36
 0-7-28
 1-18/11-9/5
 utonal
37
 0-9-28
 1-7/5-9/5
 otonal
38
 0-11-28
 1-6/5-9/5
 otonal
39
 0-17-28
 1-3/2-9/5
 utonal
40
 0-19-28
 1-9/7-9/5
 utonal
41
 0-21-28
 1-11/10-9/5
 otonal
42
 0-6-34
 1-5/4-9/8
 otonal
43
 0-7-34
 1-18/11-9/8
 utonal
44
 0-15-34
 1-7/4-9/8
 otonal
45
 0-17-34
 1-3/2-9/8
 ambitonal
46
 0-19-34
 1-9/7-9/8
 utonal
47
 0-27-34
 1-11/8-9/8
 otonal
48
 0-28-34
 1-9/5-9/8
 utonal

Tetrads

Number
 Chord
 Transversal
 Type
1
 0-2-9-11
 1-12/7-7/5-6/5
 swetismic
2
 0-2-11-17
 1-12/7-6/5-3/2
 utonal
3
 0-6-15-17
 1-5/4-7/4-3/2
 otonal
4
 0-2-9-19
 1-12/7-7/5-9/7
 swetismic
5
 0-7-9-19
 1-18/11-7/5-9/7
 swetismic
6
 0-2-12-19
 1-12/7-11/7-9/7
 otonal
7
 0-10-12-19
 1-11/6-11/7-9/7
 swetismic
8
 0-2-17-19
 1-12/7-3/2-9/7
 ambitonal
9
 0-7-17-19
 1-18/11-3/2-9/7
 utonal
10
 0-10-17-19
 1-11/6-3/2-9/7
 swetismic
11
 0-2-9-21
 1-12/7-7/5-11/10
 swetismic
12
 0-2-11-21
 1-12/7-6/5-11/10
 swetismic
13
 0-9-11-21
 1-7/5-6/5-11/10
 otonal
14
 0-2-12-21
 1-12/7-11/7-11/10
 swetismic
15
 0-6-12-21
 1-5/4-11/7-11/10
 valinorsmic
16
 0-10-12-21
 1-11/6-11/7-11/10
 utonal
17
 0-6-15-21
 1-5/4-7/4-11/10
 valinorsmic
18
 0-9-15-21
 1-7/5-7/4-11/10
 valinorsmic
19
 0-2-19-21
 1-12/7-9/7-11/10
 swetismic
20
 0-9-19-21
 1-7/5-9/7-11/10
 swetismic
21
 0-10-19-21
 1-11/6-9/7-11/10
 swetismic
22
 0-12-19-21
 1-11/7-9/7-11/10
 swetismic
23
 0-6-12-27
 1-5/4-11/7-11/8
 valinorsmic
24
 0-10-12-27
 1-11/6-11/7-11/8
 utonal
25
 0-6-15-27
 1-5/4-7/4-11/8
 otonal
26
 0-6-17-27
 1-5/4-3/2-11/8
 otonal
27
 0-10-17-27
 1-11/6-3/2-11/8
 ambitonal
28
 0-15-17-27
 1-7/4-3/2-11/8
 otonal
29
 0-6-21-27
 1-5/4-11/10-11/8
 valinorsmic
30
 0-10-21-27
 1-11/6-11/10-11/8
 utonal
31
 0-12-21-27
 1-11/7-11/10-11/8
 utonal
32
 0-15-21-27
 1-7/4-11/10-11/8
 valinorsmic
33
 0-7-9-28
 1-18/11-7/5-9/5
 swetismic
34
 0-9-11-28
 1-7/5-6/5-9/5
 otonal
35
 0-7-17-28
 1-18/11-3/2-9/5
 utonal
36
 0-11-17-28
 1-6/5-3/2-9/5
 ambitonal
37
 0-7-19-28
 1-18/11-9/7-9/5
 utonal
38
 0-9-19-28
 1-7/5-9/7-9/5
 swetismic
39
 0-17-19-28
 1-3/2-9/7-9/5
 utonal
40
 0-9-21-28
 1-7/5-11/10-9/5
 otonal
41
 0-11-21-28
 1-6/5-11/10-9/5
 otonal
42
 0-19-21-28
 1-9/7-11/10-9/5
 swetismic
43
 0-6-15-34
 1-5/4-7/4-9/8
 otonal
44
 0-6-17-34
 1-5/4-3/2-9/8
 otonal
45
 0-7-17-34
 1-18/11-3/2-9/8
 utonal
46
 0-15-17-34
 1-7/4-3/2-9/8
 otonal
47
 0-7-19-34
 1-18/11-9/7-9/8
 utonal
48
 0-17-19-34
 1-3/2-9/7-9/8
 utonal
49
 0-6-27-34
 1-5/4-11/8-9/8
 otonal
50
 0-15-27-34
 1-7/4-11/8-9/8
 otonal
51
 0-17-27-34
 1-3/2-11/8-9/8
 otonal
52
 0-7-28-34
 1-18/11-9/5-9/8
 utonal
53
 0-17-28-34
 1-3/2-9/5-9/8
 utonal
54
 0-19-28-34
 1-9/7-9/5-9/8
 utonal

Pentads

Number
 Chord
 Transversal
 Type
1
 0-2-9-11-21
 1-12/7-7/5-6/5-11/10
 swetismic
2
 0-2-9-19-21
 1-12/7-7/5-9/7-11/10
 swetismic
3
 0-2-12-19-21
 1-12/7-11/7-9/7-11/10
 swetismic
4
 0-10-12-19-21
 1-11/6-11/7-9/7-11/10
 swetismic
5
 0-6-15-17-27
 1-5/4-7/4-3/2-11/8
 otonal
6
 0-6-12-21-27
 1-5/4-11/7-11/10-11/8
 valinorsmic
7
 0-10-12-21-27
 1-11/6-11/7-11/10-11/8
 utonal
8
 0-6-15-21-27
 1-5/4-7/4-11/10-11/8
 valinorsmic
9
 0-7-9-19-28
 1-18/11-7/5-9/7-9/5
 swetismic
10
 0-7-17-19-28
 1-18/11-3/2-9/7-9/5
 utonal
11
 0-9-11-21-28
 1-7/5-6/5-11/10-9/5
 otonal
12
 0-9-19-21-28
 1-7/5-9/7-11/10-9/5
 swetismic
13
 0-6-15-17-34
 1-5/4-7/4-3/2-9/8
 otonal
14
 0-7-17-19-34
 1-18/11-3/2-9/7-9/8
 utonal
15
 0-6-15-27-34
 1-5/4-7/4-11/8-9/8
 otonal
16
 0-6-17-27-34
 1-5/4-3/2-11/8-9/8
 otonal
17
 0-15-17-27-34
 1-7/4-3/2-11/8-9/8
 otonal
18
 0-7-17-28-34
 1-18/11-3/2-9/5-9/8
 utonal
19
 0-7-19-28-34
 1-18/11-9/7-9/5-9/8
 utonal
20
 0-17-19-28-34
 1-3/2-9/7-9/5-9/8
 utonal

Hexads

Number
 Chord
 Transversal
 Type
1
 0-6-15-17-27-34
 1-5/4-7/4-3/2-11/8-9/8
 otonal
2
 0-7-17-19-28-34
 1-18/11-3/2-9/7-9/5-9/8
 utonal